# SCS

## Seminar

### Fractional Poisson motion and network traffic models

Kaj, I (Uppsala)
Thursday 17 June 2010, 15:00-16:00

Seminar Room 1, Newton Institute

#### Abstract

Packet traffic on high-speed links exhibit data characteristics consistent with long-range dependence and self-similarity. Various models have been developed where these features arise as heavy-tailed phenomena. This includes infinite source Poisson processes, on-off models and renewal type models. The typical results say that with traffic composed of a large number of aggregated sources, a-priori heavy-tailed, the fluctuations of cumulative workload behave as fractional Brownian motion, stable Lévy motion, or, bridging these two, fractional Poisson motion.

In this talk we discuss a model, which is essentially short-tailed but where job sessions are correlated with each other due to the prevailing service rates at arrival. This variation of the infinite source Poisson process is obtained from the standard M/M/$\infty$-model with exponential service rate given by the path of a mean-reverting diffusion process of CIR-type. We give a survey of the limit results for heavy-tailed models with emphasis on the role of fractional Poisson motion, and discuss preliminary results on fractional limit behavior caused by correlation in short-tailed models.

#### Video

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